Jan 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <1>
R8C2 can only be <8>
R2C5 can only be <4>
R9C5 can only be <8>
R9C1 can only be <1>
R7C2 can only be <9>
R5C2 can only be <1>
R2C2 can only be <7>
R3C2 can only be <4>
R3C7 is the only square in row 3 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R6C3 is the only square in row 6 that can be <4>
R7C4 is the only square in row 7 that can be <4>
R9C9 is the only square in row 9 that can be <4>
Squares R7C3 and R8C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C3 - removing <5> from <569> leaving <69>
Squares R9C4 and R9C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C6 - removing <2> from <235> leaving <35>
Intersection of column 9 with block 6. The values <13> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C7 - removing <13> from <1356> leaving <56>
R6C7 - removing <1> from <1567> leaving <567>
Squares R9C4, R9C6, R1C4 and R1C6 form a Type-2 Unique Rectangle on <27>.
R1C1 - removing <6> from <69> leaving <9>
R3C4 - removing <6> from <567> leaving <57>
R3C6 - removing <6> from <567> leaving <57>
R1C9 can only be <7>
R2C8 is the only square in row 2 that can be <9>
R5C8 can only be <6>
R5C1 can only be <5>
R3C8 can only be <1>
R4C7 can only be <5>
R3C3 can only be <6>
R7C8 can only be <2>
R2C7 can only be <6>
R6C7 can only be <7>
R5C5 can only be <3>
R6C1 can only be <6>
R5C9 can only be <9>
R8C5 can only be <5>
R6C9 can only be <1>
R4C3 can only be <9>
R8C7 can only be <3>
R6C4 can only be <5>
R4C9 can only be <3>
R7C3 can only be <5>
R8C8 can only be <7>
R8C3 can only be <2>
R7C6 can only be <3>
R7C7 can only be <1>
R2C3 can only be <1>
R4C6 can only be <6>
R4C4 can only be <1>
R1C6 can only be <2>
R6C6 can only be <9>
R3C4 can only be <7>
R1C4 can only be <6>
R9C6 can only be <7>
R3C6 can only be <5>
R9C4 can only be <2>
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